A Symmetric Representation for Three-Body Problems. I. Motion in a Plane

Abstract

A symmetric representation is sought for the motion of three particles in the limit of weak interaction. Operators with the desired symmetry can be obtained from the 6‐dimensional generalized angular momentumtensor [F. T. Smith, Phys. Rev. 120, 1058 (1960)]. Here, the 4‐dimensional problem of motion in a plane is worked out. Symmetric angular coordinates are found, operators and eigenfunctions are constructed, and the coupling coefficients connecting this with more familiar representations are discovered. Formally, the eigenfunctions are similar to the symmetric rotor functions, but with different arguments.